A381017 Prime terms of A000328.

5, 13, 29, 113, 149, 197, 317, 613, 709, 797, 1009, 1129, 1373, 3001, 3209, 3853, 4513, 5261, 6361, 7213, 11681, 12853, 15373, 16729, 19577, 20593, 21101, 22133, 25997, 30757, 33317, 38669, 53077, 56401, 65101, 68777, 72533, 73517, 95093, 100621, 108637, 114553, 115781, 118213

Offset

1,1

Comments

Called Gauss circle primes by Ehrenborg.

Links

Robert Israel, Table of n, a(n) for n = 1..1188

Thomas Ehrenborg, Gauss Circle Primes, arXiv:2502.06804 [math.GM], 2025. See Table 1 p. 3.

Maple

N:= 200: # for terms in A000328(1..N)
V:= Array(0..N): V[0]:= 1:
for x from 1 to N do
  for y from 0 to x do
    if y = 0 or y = x then m:= 4 else m:= 8 fi;
    s:= ceil(sqrt(x^2+y^2));
    if s > N then break fi;
    V[s]:= V[s] + m
od od:
select(isprime, ListTools:-PartialSums(convert(V, list))); # Robert Israel, May 27 2025

Prog

(PARI) select(isprime, vector(200, n, 1 + 4*sum(j=0, n^2\4, n^2\(4*j+1) - n^2\(4*j+3))))

Crossrefs

Cf. A000040, A000328, A381018.

Sequence in context: A147349 A147288 A146420 * A147492 A182069 A085555

Adjacent sequences: A381014 A381015 A381016 * A381018 A381019 A381020

Keyword

nonn

Author

Michel Marcus, Feb 12 2025

Status

approved